# vector a

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```					What’s Your Vector Victor?

or, in German, “ein-ge-vector”
Types of Quantities:
   Scalar
– size only
 speed

 mass

   Vector
– size and direction
– velocity, acceleration, momemtum
– force, pressure, torque, impulse
Expressing Vectors
   Size:

Each unit represents a set magnitude
one unit equals 10 newtons then the force
 if
vector equals 100 N
Expressing Vectors:

   Direction:
N   ___0 ___ of ___
900
Deviation - major

1800             00   W             E

2700
S
Expressing Vectors
350 N of E

250 S of W
1200

3200
   #1 Draw first vector component to scale
   #2 Start the tail of the second
component at the head of the first and
draw it
   #3 Start the tail of the resultant at the
tail of the first component and end it at
the head of the last component
C2

C1

R
C1

R

C2
C1

R

C3        C2
Two forces are applied to our little prankster!

Fb = 70 N

Fg = 65 N
Reduce our little prankster to a point and and
show both forces from that point!

Fb = 70 N                            Fg = 65 N
Reduce our little prankster to a point and and
show both forces from that point!

P
Fb = 70 N                    Fg = 65 N
Convert our point diagram to a vector diagram!

You do this by following the rules of vector addition.

P
Fb = 70 N                            Fg = 65 N
Convert our point diagram to a vector diagram!

You do this by following the rules of vector addition.

Let’s consider Fg as component one and Fb as component
two.

P
Fb = 70 N                            Fg = 65 N
Convert our point diagram to a vector diagram!

You do this by following the rules of vector addition.

Let’s consider Fg as component one and Fb as component
two.
Draw Fg first!

P
Then draw Fb
Remember, the tail              Fg = 65 N
of Fb starts at the head
of Fg
Fb = 70 N
Let’s consider Fg as component one and Fb as component
two.

Draw Fg first!

Then draw Fb

Remember, the tail
of Fb starts at the head
of Fg                           P

Draw the resultant              Fg = 65 N

Remember to start the tail
of the resultant from the tail of
Fg and ending at the head                  Fb = 70 N
of Fb
Wow, the family pet just won’t
budge! (da!)
Wow, the family pet just won’t
budge! (da!)

Dad pulls with 70 N                       Ma pulls with 65 N
Fg = 65 N
Fb = 70 N
Reduce for pet to a point!

Fg = 65 N
Fb = 70 N

P
Now draw our vector diagram!

Fb = 70 N

R

Fg = 65 N

P
Resolving Vectors
A Resultant is broken down into two or more components

R                              Cv

Ch
Sin 400 = CV / R or CV = Sin 400 (R)

Cos 400= CH / R or CH = Cos 400 (R)

R                  CV

400           CH
Graphically Analysis of Vectors
F1

F1 = 85 N at 400

F2

F2 = 75 N at 2500
Graphically Analysis of Vectors
F1
F1Y

F1X
F2

F2Y

F2X
F1
F1Y

F1X
F2
SFX = FX1 + F X2
F2Y
SFY = FY1 + FY2

F2X
F1                Fx1 = Cos q x F1 =
F1Y       Fx2 = Sin q x F2 =
400
SFx = Fx1 x Fx2 =
F1X
F2                            Fy1 = Sin q x F1 =
SFX = FX1 + F X2
200F                         Fy2 = Cos q x F2 =
2Y
SFY = FY1 + FY2
SFy = Fy1 + Fy2 =
F2X
F1
F1X
F1Y
F2X

FX                                 F1X
F2
FY
F2Y                                  SFX = FX1 + F X2

F2Y   SFY = FY1 + FY2

F1Y               F2X
FR2 = FX2 + FY2
FX
Tan 0 = FY / FX
F1X         0    FY
FR
F2X
FX

FY
F2Y

F1Y
Equilibrant Vectors
   E = -(R)

   Same size and 1800 in direction
Two-Dimensional Motion

   Projectile Motion
   Periodic Motion
Projectile Moion
Vx
Vx
Vy

Vx
Vy
Vx = constant

Vy = varying
Vy
Vx
Vx
Vy

Vx
Vy
Formulas:

Vx = constant
therefore,      Vy = varying              Vy
Vx = d/t     therefore, acceleration
vf = vi + at
d = vi + 1/2at2
Projectile Motion

Vy controls how long
vi
vy    Vy = sinq(vi)       it’s in the air and how
q                              high it goes
vx                         Vx controls how far it goes
Vx = cosq(vi)
Projectile Motion
“Range formula”
Remember!!!!!    vi is the velocity at an angle and the
sin2q is the sine of 2 x q

vi           R = vi2 sin2q/g
yi                                                              yf
Range formula works only when yi = yf
Projectile Motion
“Range formula”

R = vi2 sin2q/g
vi
If vi = 34 m/s and q is 41o then,

R = (34 m/s)2 sin82o/9.8 m/s2

R = 1160 m2/s2 (0.99)/9.8 m/s2

R = 120 m
Projectile Motion
“Range formula”

Note that if q becomes the complement
vi                  of 41o, that is, q is now 49o, then,
q   vi = 34 m/s and q is 49o then,

R = (34 m/s)2 sin98o/9.8 m/s2

R = 1160 m2/s2 (0.99)/9.8 m/s2

R = 120 m         So, both 41o and 49o yield “R”
Projectile Motion
“Range formula”

vi
vy   If vi = 34 m/s and q is 41o then,
yi                  vy = sin41o(34m/s) = 22m/s, and                        yf
vx
t = vfy - viy/g = -22m/s - (22m/s)/-9.8m/s2 = 4.5 s
vx = cos41o(34 m/s) = 26 m/s, and
dx = vx(t) = 26m/s (4.5 s) = 120 m
C1

E

C2
C1
E
C2

R        E

C1
C2
E

1/2
T1     FW      T2
T1                  T2

Cos 400 = 1/2 FW / T1

T1       800        T2        T1 = 1/2 FW / Cos 400

Al’s Food Pit

```
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 views: 15 posted: 3/9/2012 language: pages: 41